Answer to Question #232757 in Physics for jet

Question

You fill a transparent plastic bottle with conditioner. Every horizontal cross section is a circle, but the diameters of the circles have different values, so that the bottle is much wider in some places than others. You pour in bright blue conditioner with constant volume flow rate 18 cm3 /s. At what rate is its level in the bottle rising at a point where the diameter of the bottle is 8cm?

Answer 1

We know the diameter, thus, we know the cross-sectional area of this part:

$$A=\frac{\pi d^2}{4}.$$

The rate of level rise is

$$u=\frac{Q}{A}=\frac{4Q}{\pi d^2}=\frac{4·18}{3.14·8^2}=0.36\text{ cm/s}.$$